Somehow I've missed it.
TM35 Flamethrower can be found at Route 23 in Pokémon Black and White 2.
Check out this video if you want more help finding it:
Hope I helped :)
You can find flamethrower in route 23.Pass the hiker and surf on the water until you reach a house.The house should have a has ours and a man.Talk to the man and he will give it to you.